In this series of lectures, we discuss quantum many body perturbation theory from a mathematical perspective. The starting point is Feynman diagrams for Gaussian integrals. This only requires the knowledge of freshman calculus. Then assuming basic knowledge of quantum mechanics, we discuss Feynman diagrams for quantum statistical mechanics, and proceed to many body perturbation theory for fermionic systems. If time allows, we will discuss state-of-the-art computational techniques for excited state electrons such as the GW method.